A two-step convex optimization algorithm is proposed for array pattern synthesis with minimum number of antenna elements. Firstly, sparse array is synthesized based on convex optimization. Then, the optimized excitation coefficients exceeding the threshold are re-optimized again to obtain lower side lobe level. The non-uniform array and thinned array for the focused and shaped pattern have been investigated using the proposed method. Numerical comparison with other methods indicates that the proposed method has lower side lobe level in both non-uniform and thinned array.